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Deflections and Introduction to Elastic Stability
The law of conservation of energy
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applied approximate arch assumed axes axial beam and loading beam of Fig bending boundary conditions Calculate Castigliano's Theorem centroidal chapter components conjugate beam consider constant continuous beam cross section deflection of point deformations Determine diagram differential equation displacements distribution factors dummy load elastic center elastic curve elastic theory element engineering equal equilibrium example FEM's finite difference fixed-end moments flexibility matrix folded plate follows force Fortran given Hooke's Law horizontal illustrate indeterminate structures inertia joint kip-ft lb/ft longitudinal maximum method obtained plane plastic hinges problem procedure reactions redundant rigid frame rotation shear center shear stress shown in Fig sidesway sign convention simple beam simply supported simultaneous equations slope-deflection solution solved span statically indeterminate step strain energy stress distribution superposition symmetrical Table temperature theory torque torsion transverse truss unit load values vertical vertical deflection warping zero